Abstract
In a broadcast encryption system with a total of n users, each user is assigned with a unique index i ∈ [1, n]. An encryptor can choose a receiver set S ⊆ [1, n] freely and encrypt a message for the recipients in S such that only those receivers can open the message. The transmission overload of most previous broadcast encryption systems grows in line with the number of revoked users r and thus they are suitable for the scenario where the target receiver set is large when r ≪ n holds. Some other recently proposed constructions for arbitrary receiver set require a unreasonably large user storage and long decryption time. On the other hand, it is observed that, in a practical broadcast encryption system, the receiver set can be regarded as a collection of k natural intervals, where the interval number k should be much less than r for most cases. This observation motivates us to introduce a novel type of encryption, called interval encryption, which could realize a more efficient broadcast encryption. To achieve this, we first present a generic way to transform a binary tree encryption scheme into interval encryption. One concrete instantiation of this method based on the hierarchical identity based encryption scheme by Boneh et al. only requires a \(\mathcal{O}(k)\) transmission cost and \(\mathcal{O}(\log n)\) private storage consumption, while the decryption is dominated by \(\mathcal{O}(\log n)\) group operations. With detailed performance analysis, we demonstrate that the proposed interval encryption strategy has the superiority on improved efficiency and thus is expected to serve as a more efficient solution in more cases than the traditional systems in practice. Interestingly, our methodology can also be employed to transform a fully secure hierarchical identity based encryption scheme proposed by Lewko and Waters into an adaptively secure interval encryption scheme with a \(\mathcal{O}(k)\) transmission cost and \(\mathcal{O}(\log n)\) private storage consumption. Finally, we also discuss several other promising applications of interval encryption.
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Lin, H., Cao, Z., Liang, X., Zhou, M., Zhu, H., Xing, D. (2010). How to Construct Interval Encryption from Binary Tree Encryption. In: Zhou, J., Yung, M. (eds) Applied Cryptography and Network Security. ACNS 2010. Lecture Notes in Computer Science, vol 6123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13708-2_2
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DOI: https://doi.org/10.1007/978-3-642-13708-2_2
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